Strict embedding of the elementary ontology into the monadic second-order calculus of predicates admitting the empty individual domain

Studia Logica 46 (1):1 - 15 (1987)
Abstract
There is given the proof of strict embedding of Leniewski's elementary ontology into monadic second-order calculus of predicates providing a formalization of the class of all formulas valid in all domains (including the empty one). The elementary ontology with the axiom S (S S) is strictly embeddable into monadic second-order calculus of predicates which provides a formalization of the classes of all formulas valid in all non-empty domains.
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DOI 10.1007/BF00396902
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